3 papers
math.CO2026
Tracks on planar complexes and soficity
Hiroki Ishikura
We show that every probability-measure-preserving equivalence relation generated by a locally-finite Borel graph with planar connected components is sofic in the sense of Elek--Lip…
math.GR2025
Decomposition of Borel graphs and cohomology
Hiroki Ishikura
We give a cohomological criterion for certain decomposition of Borel graphs, which is an analog of Dunwoody's work on accessibility of groups. As an application, we prove that a Bo…
math.GR2023
Free metabelian groups are permutation stable
Hiroki Ishikura
We prove that all finitely generated free metabelian groups are permutation stable. This partially answers to the question asked by Levit and Lubotzky whether all finitely generate…